Solve the inequality.
-For the function $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$, solve $h ( x )

Question

Solve the inequality.
-For the function $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$, solve $h ( x ) < 0$.
A) $( - \infty , 2 ) \cup ( 6 , \infty )$
B) $( - \infty , 0 ) \cup ( 2,6 )$
C) $[ 2,6 ]$
D) $( - \infty , 2 ] \cup [ 6 , \infty )$

Quizplus · Accepted Answer

To solve $h(x) < 0$, we need to determine where the function is negative. The denominator $(x-2)(x-6)$ changes sign at $x = 2$ and $x = 6$, and the numerator $2x$ changes sign at $x = 0$. Between $x = 2$ and $x = 6$, the function is negative because the signs of the numerator and denominator are different (numerator positive, denominator negative). Outside these points, the function is positive. Therefore, the solution is $( - \infty , 0 ) \cup ( 2,6 )$.

Solve the Inequality h(x)=2x(x−2)(x−6)h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }h(x)=(x−2)(x−6)2x​

Solve the Inequality $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$